We've recently migrated from sharing one Apple ID to Family Sharing.
With Family Sharing, each family member signs into his or her own Apple ID, but shares calendars, etc. with the main Apple ID, managed by the "Organizer."

It took a while, but I think we got most everything figured out. We were reminded today, however, that Reminders was still not doing what what we wanted. Here's what I figured out:

1. When you set up Family Sharing, everyone in the family gets a Family list in Reminders. You don't have a choice about this, but apparently you can rename this list. We decided that would replace our Miscellaneous list.
2. To share other Reminders lists, the organizer can look at Reminders on the Mac, click the broadcast icon next to the list name and select the person to share with, by name or Apple ID. You can do this on an iPhone or iPad, but it seems easier to me to do it on the Mac.
3. Every account must have at least one Reminders list owned by the account owner. That means that another family member cannot have only Reminders lists shared by the organizer. I see two ways to deal with this. First, the family member who's not the organizer can just ignore the required Reminders list, named, by default, Reminders. Second, the the family member who's not the organizer can share their required list (renamed if desired) and replace another list the family is used to. So that means the organizer would share some lists, and each family member would share at least one list.

[Additional]
I think we've got this done now. A goal was to pare down the number of separate lists we had, especially since switching to Family Sharing added two.*
I'm the account "owner," so I changed the name of Family. That, apparently counts as the account I own, so I don't get another one added automatically. And it's automatically shared.
My wife changed the name of Reminders and shared it with me.
We deleted all other lists, leaving us with the desired two. All these changes propagated to both our Macs, both logins for iCloud, my iPhone and our iPad. We had to change the names manually on my wife's iPhone for some unknown reason.

* Users' desires will vary, of course, but I think when you're beginning with Reminders, it's easy to create too many lists. That requires you to look at too many lists or set notifications so you don't forget.

"Design is not just what it looks like and feels like. Design is how it works."
Steve Jobs